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The tape and δ Tape is infinite in both directions –Blanks straddle the input on the tape. Begin reading at leftmost input symbol. As soon as you enter accept state, halt. –You don’t have to read all the input. δ (state, input) = (state, output, direction) –You may change state. –You may change the symbol that’s on the tape. –The “direction” is either L or R.

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States A TM has at least 3 states –One accept state –One reject state –Ordinary states that we describe in our transition table, beginning with a start state. We don’t need transitions for the accept or reject states. Sometimes a transition “doesn’t matter” because we can’t be in that situation. –Ex. If the leftmost symbol isn’t blank, then the rightmost symbol can’t be blank. You can just go to reject state.

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Infinite loop It’s possible for a TM to have an infinite loop. We say that the TM “loops.” In this case, it doesn’t accept or reject its input. Simple example: From start state, go left on any input! StateInput 0Input 1Input _ s1s1, 0, Ls1, 1, Ls1, _, L

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Mystery #1 What does this TM do? Assume s1 is the start state, and unspecified transitions are crash. StateInput 0Input 1Input _ s1s2, 1, R s2s1, 0, R Hint: notice we never move left. This means it doesn’t matter what we write on tape.